We report the first measurement of the full angular distribution for inclusive J/ψ → μ⁺μ⁻ decays in p + p collisions at √s=510 GeV. The measurements are made for Jψ transverse momentum 2 < p_T < 10 GeV/c and rapidity 1.2 < y < 2.2 in the Helicity, Collins-Soper, and Gottfried-Jackson reference frames. In all frames the polar coefficient λ_θ is strongly negative at low p_T and becomes close to zero at high pT, while the azimuthal coefficient λ_ϕ is close to zero at low pT, and becomes slightly negative at higher p_T. The frame-independent coefficient λ is strongly negative at all p_T in all frames. The data are compared to the theoretical predictions provided by nonrelativistic quantum chromodynamics models.